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| 11:30 | – | 12:30 | | Introductory talk — Tim Riley, Bristol |
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What is amenability? What is a Dehn function? |
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This two-part talk will be aimed at graduate students and researchers from other fields, and will be intended to provide some background for the main talks. |
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We will discuss recent developments
concerning growth of amenable groups. |
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Amenability at infinity for discrete groups |
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Property A is a non-equivariant analogue of amenability defined by Guoliang Yu for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. The methods allow us to give a strengthened form of a result of Caprace concerning amenability for stabilisers at infinity for groups acting properly on a finite-dimensional CAT(0) cube complex. |
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A polynomial Dehn function for SL(n,Z) |
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It is known that SL(2,Z) is hyperbolic and has a linear Dehn function, and that SL(3,Z) contains a solvable group in such a way that its Dehn
function is exponential, but the behavior of the Dehn function in
higher dimensions has been a long-open conjecture. In this talk, I
will describe some of the background of the problem and some of the
geometry of the quotient SL(n,Z)\SL(n,R), and use this geometry to
sketch a proof that SL(n,Z) has a quartic Dehn function for n at least 5. |
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